Communications in Mathematical Physics

, Volume 69, Issue 2, pp 131–146 | Cite as

Fonctions Propres et Non-Existence Absolue D'Etats Liés dans Certains Systèmes Quantiques

  • Bernard Gaveau


One proves a condition of absence of bound states for a Schrödinger operator independent of any self-adjoint extension. The method of proof uses Feynman Kac formula.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Berthier, A.M., Gaveau, B.: Critère de convergence des fonctionnelles de Kac et applications en mécanique quantique et en géométrie. J. Funct. Anal.30, 310 (1978)Google Scholar
  2. 2.
    Glaser, V., Martin, A., Grosse, H., Thirring, W.: A family of optimal conditions for the absence of bound states. Symposium in honor of V. Bargman. Princeton U. p. 169–194 (1976)Google Scholar
  3. 3.
    Kac, M.: On some connections between probability and differential equations. 2nd Berkeley Symposium on probability and statistics 1950Google Scholar
  4. 4.
    Kato, T.: Math. Ann.162, 258 (1966)Google Scholar
  5. 5.
    Klein, A., Laudau, F.: J. Funct. Anal.20 (1975)Google Scholar
  6. 6.
    McKean, H.: Stochastic integrals. New York: Academic Press 1969Google Scholar
  7. 7.
    Simon, B.: On the number of bound states of two body Schrödinger equations: a review. Symposium in honor of V. Bargmann. Princeton (1976)Google Scholar
  8. 8.
    Vauthier, J.: À paraîtreGoogle Scholar

Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • Bernard Gaveau
    • 1
  1. 1.Université P. et M. Curie (Mathématiques)Paris Cedex 05France

Personalised recommendations